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Loose Engel structures

Published online by Cambridge University Press:  06 January 2020

Roger Casals
Affiliation:
University of California Davis, Department of Mathematics, Shields Avenue, Davis, CA 95616, USA email casals@math.ucdavis.edu
Álvaro del Pino
Affiliation:
Utrecht University, Department of Mathematics, Budapestlaan 6, 3584 CD Utrecht, The Netherlands email a.delpinogomez@uu.nl
Francisco Presas
Affiliation:
Instituto de Ciencias Matemáticas – CSIC, C. Nicolás Cabrera 13–15, 28049 Madrid, Spain email fpresas@icmat.es

Abstract

This paper contributes to the study of Engel structures and their classification. The main result introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This implies a complete $h$-principle when auxiliary data is fixed. As a corollary, we show that Lorentz and orientable Cartan prolongations are classified up to homotopy by their formal data.

Type
Research Article
Copyright
© The Authors 2020

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